I stumbled on this thread as I was troubleshooting my own icing anomalies in the Fenix A320.
So, a couple of things from my time in the Bus and Boeing (bear in mind that I haven’t flown a RL 737 in about 14 years):
As far as I can remember, both AC have electrically heated windows (i.e. they work more like your car’s rear window than your front). There are some AC that have hot air blowing on your front windscreen, but I don’t remember that being the case in either of these two AC. At least, not as your primary defrosting mechanic.
FWIW, I flew the B-737-200/300/500/700 (so…older) and the A319/320/321 (newer and more recently), just as a gauge.
As such, I’m a little confused about the comment that turning on your APU is necessary to deice the AC, particularly the windows for the reason I stated. For one thing, I seem to recall that the engine AI in either AC is provided by its own bleed air, usually through a primary and auxiliary bleed valve. So, I’m not even certain that you could get APU air to either EAI system.
As far as WAI goes, I believe both the Bus and Boeing use air from the bleed system (to which the APU is attached through its own bleed valve). But, considering that in either case the only thing that you are applying heat to are portions of the leading edge, you’re not really deicing much. Moreover, I know that the Bus cautions you against using APU bleed to deice the wings. I wouldn’t be surprised (but can’t remember) if the 737 wasn’t the same.
That all being said, with the exception of a cold and dark start on a snowy ramp, the electrically heated windows always seemed to work famously…for the same reason they work on your rear window. Bear in mind that I have primarily flown in CONUS; a Norwegian Bus/Boeing driver may give you a different answer! 
None of that will have any effect on the rest of your aircraft however. It will be covered by snow and ice until you deice it. It really can’t be deiced by itself. The primary initial concern is usually the engines. I’ve heard of various methods of defrosting them (e.g. hot air) but, if you can get her off the gate, then you can taxi down to the deicing pits.
Once there, you should have most of your concerns addressed…at least until the holdover time has expired.
There are, of course, things you must consider when you’re operating in these conditions, but generally it works quite well.
As to filing/operating in icing conditions enroute, the dispatcher and pilot in command share joint operational authority. Bear in mind that, just because there is icing forcasted/reported in an area, that doesn’t mean that it is occurring at all altitudes within that area. For instance, yesterday there was a wide swath of moderate icing forecast along the US eastern seaboard, but only between the surface and 20,000ft. Since most jet flights operate above that altitude, there’s likely no reason that enroute operations couldn’t fly through there.
Moreover, just because there is icing forecast in an area, doesn’t mean that aircraft can’t operate there at all. It just means that flight crews and controllers may need to consider, plan for, and be prepared for icing to occur.
I wouldn’t want to fly a C-152 through those areas. But most airliners are capable of operating in at least moderate icing conditions…with potentially some restrictions.
On the other hand, all the operators that I have worked for have had a prohibition (likely FAA standard) against operating in known or forecast severe icing conditions. Luckily, that doesn’t occur very often…at least in temperate latitudes.
Lastly, and I apologize for how long this is, from the reason that I found myself here, I think that MSFS can exaggerate icing a bit. Flying the excellent Fenix A320, I encountered icing at approach altitudes in both IAD and LGA in the last two days that overwhelmed the pitot heating capability of the Bus. Historically, this isn’t unheard of, but it feels unlikely on two subsequent days.
I understand from reading above that this is a Fenix…ism. But, having switched to the default Asobo A320, it shortly did the same thing.
So, just something to keep in mind when you are flying these larger, more capable, aircraft in MSFS that things may be modelled more, dramatically, than is strictly accurate.
